Predict Power from VO2 with RER and GE

Thread posted

Common question I hear: "My VO2max is x and my current threshold power is y. Is it possible for me to reach an FTP of z?”

It's surprisingly simple to predict power from VO2, and vice versa

We just need reasonable estimates for RER substrate oxidation and metabolic efficiency 📊🧵/4 #rstats #datavis

[image or embed]

— Jem Arnold (@jemarnold.bsky.social) 8 January 2026 at 14:11

library(tidyverse)
library(geomtextpath)
library(ggtext)
library(colorspace)
library(sysfonts)
library(showtext)

## use font & icons in ggplots
sysfonts::font_add_google(
    name = "Merriweather Sans", 
    family = "Merriweather Sans"
)
sysfonts::font_add(
    family = "fa-brands", 
    regular = r"(C:\Users\Jem\AppData\Local\Microsoft\Windows\Fonts\Font Awesome 7 Brands-Regular-400.otf)"
)
showtext::showtext_opts(dpi = 600)
showtext::showtext_auto()

## custom theme
theme_set(
    theme_bw(base_size = 12, base_family = "Merriweather Sans") +
        theme(
            plot.title = ggtext::element_textbox_simple(
                size = rel(1.2), lineheight = 1.1
            ),
            plot.subtitle = ggtext::element_textbox(
                colour = "grey35", face = "italic", hjust = 0, 
                lineheight = 1.1, margin = margin(b = 4)
            ),
            plot.caption = ggtext::element_textbox(
                colour = "grey35", halign = 1
            ),
            panel.border = element_rect(linewidth = 0.8),
            axis.title = element_text(face = "bold"),
            panel.grid.major = element_blank(),
            panel.grid.minor = element_blank(),
            legend.position = "none"
        )
)

social_caption <- "<span style='font-family:fa-brands'>&#xf09b; &#xe671;</span> jemarnold"

Post 1

Common question I hear: “My VO2max is x and my current threshold power is y. Is it possible for me to reach an FTP of z?”

It’s surprisingly simple to predict power from VO2, and vice versa

We just need reasonable estimates for RER substrate oxidation and metabolic efficiency 📊🧵/4 #rstats #datavis

VO2max_rel <- 71 ## ml/kg/min
weight <- 71 ## kg
VO2max <- VO2max_rel / 1000 * weight ## ≈ 5.0 L/min
power <- seq(300, 400, by = 10) ## W
RER <- seq(0.85, 0.95, 0.02) ## RER at threshold
GE <- (0.04824536 * log(power) - 0.05657161) + 0.025 ## % derived from Ettema & Lorås, 2009
GE <- round(seq(min(GE) - 0.025, max(GE) + 0.025, 0.01), 2)
GE <- seq(0.2, 0.25, 0.01) ## use pretty GE range anyway

df <- expand_grid(power, RER, GE) |>
    mutate(
        O2kJ = 4.83535 * RER + 16.88348, ## kJ/L derived from Péronnet & Massicotte, 1991
        VO2 = (power * 60 / 1000) / (GE * O2kJ), ## L/min
        VO2_rel = VO2 / VO2max, ## %
    )

ggplot(df, aes(x = power, y = VO2_rel, group = interaction(RER, GE), colour = factor(GE))) +
    labs( ## labs use markdown formatting with {ggtext}
        title = "Is it possible to achieve **380+ W** FTP at **5.0 L/min** VO<sub>2</sub>max?",
        subtitle = "Physiologically yes, with elite efficiency & fractional threshold.",
        caption = str_glue(
            "**Data**: derived from stochiometric equations | **Visuals**: {social_caption}"
        )
    ) +
    coord_cartesian(ylim = c(NA, 1)) +
    scale_x_continuous(
        name = "Functional Threshold Power (W)",
        breaks = power,
        expand = expansion(0.01)
    ) +
    scale_y_continuous(
        name = expression(bold(
            Percent~of~VO['2']*max~'@ 5.0'~L*'·'*min^'-1'~'(%)'
        )),
        label = scales::percent_format(suffix = ""),
        n.breaks = 6,
        expand = expansion(c(0.01, 0))
    ) +
    geom_hline(yintercept = 0.9, linetype = "dashed", colour = "grey60") +
    geom_vline(xintercept = 380, linetype = "dotted", colour = "grey60") +
    geom_line() +
    geomtextpath::geom_textline(
        data = ~ filter(.x, GE == rev(GE)[1L] & RER == 0.85),
        aes(
            label = str_glue("{round(GE*100)}% Gross Metabolic Efficiency"),
            colour = stage(factor(GE), after_scale = colorspace::darken(colour, 0.2))
        ),
        linewidth = 0, size = 4, hjust = 0.15, halign = "left", vjust = 0.2
    ) +
    geomtextpath::geom_textline(
        data = ~ filter(.x, GE != rev(GE)[1L] & RER == 0.85),
        aes(
            label = str_glue("{round(GE*100)}%"),
            colour = stage(factor(GE), after_scale = colorspace::darken(colour, 0.2))
        ),
        linewidth = 0, size = 4, hjust = 0.1, halign = "left", vjust = 0.1
    ) +
    geomtextpath::geom_textline(
        data = ~ filter(.x, GE == rev(GE)[1L] & RER == 0.95),
        aes(
            label = "(colour bands represent RER range = 0.85 - 0.95)",
            colour = stage(factor(GE), after_scale = colorspace::darken(colour, 0.15))
        ),
        linewidth = 0, size = 3.0, hjust = 0.15, halign = "left", vjust = 1.1
    )

Post 2

Reasonable estimates for gross metabolic efficiency (GE) for trained cyclists is 15-25%

GE logarithmically increases with power output, so higher fitness = higher power = higher GE

Prediction model: GE = 0.0482 * log(power) - 0.0566

90% prediction interval for individual values is around ± 2.5%

Post 3

GE prediction model derived from data in Ettema & Lorås, 2009 (link in 📊Alt text)

Most of the variance in GE comes from differences in cadence. Most of the rest comes from random cross-sectional individual differences

GE is probably trainable, but veeery slowly

Post 4

Typical reported range for fractional threshold (%VO2max @ CP, FTP, MLSS, VT2, LT2, etc) in trained cyclists is anywhere from 75-90%+, possibly higher in elite and female athletes

I can’t find a good dataset for cyclists right now, so here is one for treadmill running (link & details in 📊Alt text)

Post 5

RER is a function of exercise intensity and substrate (lipid/glucose) oxidation

At threshold, RER will be ~0.85-0.95, maybe up to 1.00 by the end.

Along each GE isoline in the top figure, RER equates to a small difference of 2 %VO2max. GE drives the big differences

Post 6

So for this specific question “is it possible to achieve an FTP of 380 W at 5.0 L/min VO2max?”

The answer is yes, with elite-level metabolic efficiency ~24% and fractional threshold ~90%VO2max

*How* to achieve that is an entirely different question which I don’t have code for (yet 😉)